A:The Bible says that Ahaziah was king of Israel for about two years (approx 852-851 BCE). Another Ahaziah is recorded as king of Judah for one year (approx 843-842 BCE).
Ahab's successors in Israel were his sons Ahaziah (parts of two years) and Jehoram (roughly seven according to 2 Chronicles, though the Deuteronomist gives him twelve years). In Judah, Jehoram, son of Jehoshaphat reigned for at least seven years and Jehoram's son Ahaziah for less than a year. This means that Ahaziah and Jehoram ruled Israel for about eight years, and also that Jehoram and Ahaziah ruled Judah during approximately the same eight years.
The duplication of the names, even if in reverse order, is startling and has led to speculation that Judah was really under Israelite rule for this period, which the southern scribes were unwilling to acknowledge. We will probably never know for certain, but it is possible that Ahaziah, son of Ahab, really was king of both Israel and a defeated Judah (followed by his brother Jehoram).